A formal solution of the telegraph problem if ∂ 2 u ∂ t 2 + ∂ u ∂ t + u = α 2 ∂ 2 u ∂ x 2 , 0 < x < L , t > 0 , u ( 0 , t ) = u ( L , t ) = 0 , t > 0 , u ( x , 0 ) = f ( x ) , 0 < x < L , ∂ u ∂ t ( x , 0 ) = 0 , 0 < x < L .

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Chapter 10.6, Problem 11E

To determine

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²

2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).

3. We'd like to know the first time when the population reaches 7000 people. First, graph the function from part (a) on your calculator or Desmos. In the same window, graph the line y = 7000. Notice that you will need to adjust your window so that you can see values as big as 7000! Investigate the intersection of the two graphs. (This video shows you how to find the intersection on your calculator, or in Desmos just hover the cursor over the point.) At what value t> 0 does the line intersect with your exponential function? Round your answer to two decimal places. (You don't need to show work for this part.) (2 points)

Answer 2

Question

Chapter 10.6, Problem 11E

To determine

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

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Answer 3

Question

Chapter 10.6, Problem 11E

To determine

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

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Answer 4

Question

Chapter 10.6, Problem 11E

To determine

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

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Answer 5

Chapter 10.6, Problem 11E

To determine

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

Answer 6

Chapter 10.6, Problem 11E

To determine

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

Answer 7

Chapter 10.6, Problem 11E

To determine

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 6E Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...

A formal solution of the telegraph problem if ∂ 2 u ∂ t 2 + ∂ u ∂ t + u = α 2 ∂ 2 u ∂ x 2 , 0 < x < L , t > 0 , u ( 0 , t ) = u ( L , t ) = 0 , t > 0 , u ( x , 0 ) = f ( x ) , 0 < x < L , ∂ u ∂ t ( x , 0 ) = 0 , 0 < x < L .

Solution Summary: The author explains that the formal solution of the telegraph problem is u(x,t)=displaystyle undersetn=1

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

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Chapter 10 Solutions

A formal solution of the telegraph problem if ∂ 2 u ∂ t 2 + ∂ u ∂ t + u = α 2 ∂ 2 u ∂ x 2 , 0 &lt; x &lt; L , t &gt; 0 , u ( 0 , t ) = u ( L , t ) = 0 , t &gt; 0 , u ( x , 0 ) = f ( x ) , 0 &lt; x &lt; L , ∂ u ∂ t ( x , 0 ) = 0 , 0 &lt; x &lt; L .

Solution Summary: The author explains that the formal solution of the telegraph problem is u(x,t)=displaystyle undersetn=1

A formal solution of the telegraph problem if ∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.

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Chapter 10 Solutions

A formal solution of the telegraph problem if ∂ 2 u ∂ t 2 + ∂ u ∂ t + u = α 2 ∂ 2 u ∂ x 2 , 0 < x < L , t > 0 , u ( 0 , t ) = u ( L , t ) = 0 , t > 0 , u ( x , 0 ) = f ( x ) , 0 < x < L , ∂ u ∂ t ( x , 0 ) = 0 , 0 < x < L .

A formal solution of the telegraph problem if

∂2u∂t2+∂u∂t+u=α2∂2u∂x2, 0<x<L, t>0,u(0,t)=u(L,t)=0, t>0,u(x,0)=f(x), 0<x<L,∂u∂t(x,0)=0, 0<x<L.